Convergence results on the general inertial Mann–Halpern and general inertial Mann algorithms

Fixed Point Theory and Applications Pub Date : 2023-12-08 DOI:10.1186/s13663-023-00752-z

Solomon Gebregiorgis, Poom Kumam

引用次数: 0

Abstract

In this paper, we prove strong convergence theorem of the general inertial Mann–Halpern algorithm for nonexpansive mappings in the setting of Hilbert spaces. We also prove weak convergence theorem of the general inertial Mann algorithm for k-strict pseudo-contractive mappings in the setting of Hilbert spaces. These convergence results extend and generalize some existing results in the literature. Finally, we provide examples to verify our main results.

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一般惯性曼-哈尔彭算法和一般惯性曼算法的收敛结果

在本文中，我们证明了在希尔伯特空间环境中针对非展开映射的一般惯性曼-哈尔帕恩算法的强收敛定理。我们还证明了在希尔伯特空间环境中 k 严格伪收缩映射的一般惯性 Mann 算法的弱收敛定理。这些收敛结果扩展和概括了文献中的一些现有结果。最后，我们举例验证了我们的主要结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.